# Targetless Extrinsic Calibration of Multiple Small FoV LiDARs and Cameras using Adaptive Voxelization

arXiv: https://arxiv.org/abs/2109.06550 · HTML: https://mlsanity.com/paper/2109.06550/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2021.

## Built on by (most cited first, 9 of 9)

- [InfraDet3D: Multi-Modal 3D Object Detection based on Roadside Infrastructure Camera and LiDAR Sensors](https://mlsanity.com/paper/2305.00314/) (2023)
- [UniCal: Unified Neural Sensor Calibration](https://mlsanity.com/paper/2409.18953/) (2024)
- [OmniColor: A Global Camera Pose Optimization Approach of LiDAR-360Camera Fusion for Colorizing Point Clouds](https://mlsanity.com/paper/2404.04693/) (2024)
- [CMR-Agent: Learning a Cross-Modal Agent for Iterative Image-to-Point Cloud Registration](https://mlsanity.com/paper/2408.02394/) (2024)
- [CalibRefine: Deep Learning-Based Online Automatic Targetless LiDAR-Camera Calibration with Iterative and Attention-Driven Post-Refinement](https://mlsanity.com/paper/2502.17648/) (2025)
- [PSS-BA: LiDAR Bundle Adjustment with Progressive Spatial Smoothing](https://mlsanity.com/paper/2403.06124/) (2024)
- [YOCO: You Only Calibrate Once for Accurate Extrinsic Parameter in LiDAR-Camera Systems](https://mlsanity.com/paper/2407.18043/) (2024)
- [CaLiV: LiDAR-to-Vehicle Calibration of Arbitrary Sensor Setups](https://mlsanity.com/paper/2504.01987/) (2025)
- [Galibr: Targetless LiDAR-Camera Extrinsic Calibration Method via Ground Plane Initialization](https://mlsanity.com/paper/2406.11599/) (2024)

## Abstract (arXiv)

Determining the extrinsic parameter between multiple LiDARs and cameras is essential for autonomous robots, especially for solid-state LiDARs, where each LiDAR unit has a very small Field-of-View (FoV), and multiple units are often used collectively. The majority of extrinsic calibration methods are proposed for 360^circ mechanical spinning LiDARs where the FoV overlap with other LiDAR or camera sensors is assumed. Few research works have been focused on the calibration of small FoV LiDARs and cameras nor on the improvement of the calibration speed. In this work, we consider the problem of extrinsic calibration among small FoV LiDARs and cameras, with the aim to shorten the total calibration time and further improve the calibration precision. We first implement an adaptive voxelization technique in the extraction and matching of LiDAR feature points. Such a process could avoid the redundant creation of k-d trees in LiDAR extrinsic calibration and extract LiDAR feature points in a more reliable and fast manner than existing methods. We then formulate the multiple LiDAR extrinsic calibration into a LiDAR Bundle Adjustment (BA) problem. By deriving the cost function up to second-order, the solving time and precision of the non-linear least square problem are further boosted. Our proposed method has been verified on data collected in four targetless scenes and under two types of solid-state LiDARs with a completely different scanning pattern, density, and FoV. The robustness of our work has also been validated under eight initial setups, with each setup containing 100 independent trials. Compared with the state-of-the-art methods, our work has increased the calibration speed 15 times for LiDAR-LiDAR extrinsic calibration and 1.5 times for LiDAR-Camera extrinsic calibration (averaged result from 50 independent trials) while remaining accurate.